In addition to Gephi, there are many network graph toolkits available in the open source space. The following list is not exhaustive, but provides a number of options for tools that can also be used to generate network graphs:
NodeXL is an Excel-based network graph software available at http://nodexl.codeplex.com/.
Cytoscape is an open source network graph software that was originally designed for biological use, but now has an expanded scope. It is available at http://www.cytoscape.org/.
Jung is a java-based open source network graph framework at http://jung.sourceforge.net/.
GUESS is a Python-based software for graph exploration at http://graphexploration.cond.org/.
Pajek is a Windows-based program designed for large network analysis at http://pajek.imfm.si/doku.php?id=pajek.
GraphML is one of the older graph projects available, with fewer recent updates than most of the tools in this list at http://graphml.graphdrawing.org/.
D3 is a JavaScript-based tool that contains some network-based components http://d3js.org/.
SigmaJS is an alternative to D3 offering some similar options for creating network-based visualizations at http://sigmajs.org/.
Ora is another tool designed for network analysis and graphs, and is part of the CASOS project at Carnegie-Mellon. You can download Ora at http://www.casos.cs.cmu.edu/projects/ora/.
There are other tools beyond this list, but these will give you a good idea for that's happening in the network visualization arena.